SHANGHAI—Gap Inc., a clothing company well-known to the U.S. middle class, is expanding across China. It is a thriving market for retailers, but the competition is increasingly fierce. Knowing how to shift business strategy to adapt to local demands is key.

The San Francisco company, which operates Gap, Old Navy, Banana Republic and Athleta brands, plans to open 25 Gap stores and up to 10 Gap outlet stores in China in 2014, adding to...